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The Quarterly Journal of Mechanics and Applied Mathematics 1981 34(4):431-451; doi:10.1093/qjmam/34.4.431
© 1981 by Oxford University Press
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LOW-FREQUENCY SCATTERING IN ELASTICITY

D. S. JONES

( Department of Mathematics, The University Dundee, DD1 4HN )

When a non-uniformity in a homogeneous isotropic elastic body is subjected to an incoming harmonic wave of low frequency, the scattered field can be expressed in terms of static approximations of which the first was given by Rayleigh. To assess the accuracy of the first approximation, bounds are derived together with estimates of the effect of changing the material constants and shape of the inhomogeneity. Variational principles are also exhibited. An explicit formula for the second level of approximation which evades solving an additional static problem is acquired. An approximate solution which is both convergent and stable, with a posteriori bounds to the error, is described.


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